1. Field of the Invention
This invention generally relates to a transmissive, rear-illuminated twisted-nematic (TN) color liquid crystal display (LCD) employing a special front fiber-optic faceplate or optical equivalent that increases the effective viewing angle between the display and a viewer while minimizing undesirable variations in display chromaticity, luminance, and contrast ratio. In particular, the front fiber-optic faceplate or optical equivalent includes masked interstitial apertures or opaque fiber cladding material.
2. Description of Related Art
A conventional, transmissive direct-view color LCD is composed of a source of illumination and a multitude of layered optical elements which each modify the spectral composition of light originating from the source. Moreover, some of these elements, such as polarizers, retardation films and the liquid crystal (LC) layer itself, are optically anisotropic and birefringent layers which produce complex spectral modifications that vary as a function of the material parameters and construction of the LC cell, display voltage (i.e., luminance or gray level), and the direction of light propagation. The predominant LC cell configuration for high-performance color LCDs is the twisted-nematic cell. In the TN cell, incoming light is initially linearly polarized by an entrance polarizer and then the axis of polarization is optically rotated by the LC layer. The rotation of the axis of polarization is mediated by the bifringence and thickness of the LC layer. The typical twist or rotation angle used for most TN LCDs is 90.degree., although other twist angles may be used to achieve certain desired optical characteristics. After optical rotation by the LC layer, the polarization state of light exiting the LC layer is analyzed by the exit polarizer or "analyzer." Two principle configurations of TN cell entrance and exit polarizers are used, LCDs that utilize crossed polarizers are often called normally-white (NW) mode LCDs while those consisting of parallel polarizers are typically called normally-black (NB) mode LCDs. For both voltage-controlled gray scale and off-axis viewing, the light path through the LC layer "sees" a different birefringence than in the fully voltage-saturated, on-axis situation. This is due to the fact that the angles at which the light path intercepts the anisotropic LC molecules vary as a function of LC cell voltage and viewing angle. This in turn results in different degrees of stimulation of the ordinary and extraordinary modes of the LC causing varying degrees of phase difference between the two polarization components, different polarization states at exit from the LC cell, and resulting variations in light transmission through the exit polarizer. In addition, phase differences between polarization components and resulting variations in light transmission are wavelength dependent, thereby resulting in chromaticity differences as well as intensity or luminance differences. Off-axis viewing adds additional complications due to path length differences through all of the material layers comprising the LCD as well as angle-related reflection and polarization effects at all of the different optical boundaries.
As such, LCDs, and in particular TN color LCDS, exhibit undesirable variations in luminance, contrast ratio and chromaticity as a function of the viewing angle between the display and an observer. Moreover, since both off-axis viewing and voltage-controlled gray scale result in variations in display luminance, contrast ratio and chromaticity, the combination of these two factors further accentuates the anisotropies evident in direct-view TN LCDs. In some instances, i.e., at particular combinations of viewing-angle and voltage-controlled gray level, the contrast ratio of the display may actually reverse and the desired color may shift to a complementary hue. Obviously, these anisotropies in display visual characteristics greatly limit the useful angular viewing cone of the display, especially for direct-view TN color LCDs employing voltage-modulated gray level control. Thus, while this LCD configuration has many desirable operating characteristics and is thus the commonplace for high-performance direct-view color LCDs (often employing an active-matrix addressing substrate to facilitate high-resolution/high-contrast operation), viewing angle limitations severely compromise the ultimate imaging performance achievable with this display device.
A number of potential solutions to ameliorate viewing angle problems in direct-view LCDs have been proposed; including the use of a diffusing optical layer at the output of the LCD, three-dimensional retardation films or optical compensators e.g., Ong, H. L. (1993). Negative-Birefringence Film-Compensated Multi-Domain TNLCDs with Improved Symmetrical Optical Performance. SID Digest of Technical Papers, 658-661!, and so-called multi-domain pixel structures Tanuma, S. (1988). Japan Patent No. 63-106624; Otani, A. (1989). Japan Patent No. 0188520!. The use of a diffusing optical layer (e.g., ground-glass scattering screen) at the output of the LCD would result in a de-coupling of the LCD from the viewing direction; however, such a diffusing element would scatter light from both directions and would severely degrade LCD image contrast under incident ambient illumination, which is typical for most office and outdoor environments. Retardation films or optical compensators can produce some useful improvements in LCD viewing angle; however, the phase retardation imparted to the light propagating through the film is highly wavelength sensitive and can thus only compensate for a limited portion of the visible spectrum. This limits the effectiveness of retardation films or optical compensators when used for improving the viewing angle of full-color displays. Finally, relatively recent developments in multi-domain pixel structures, which are optically self-compensating alignments within the LC cell, can prove to be highly effective at improving the viewing angle of direct-view color LCDs. Unfortunately, such alignments can be difficult to establish precisely and also significantly complicate the manufacture of the LC cell. In addition, there is a tendency for the domain or alignment boundaries to appear as visible borders, patterns and striations in the display, thereby degrading the image quality of the LCD.
Typical color LCD displays use a patterned, mosaic of color selection filters created within the LC cell itself. In addition, a subtractive or stacked color LCD configuration can be created with three sequentially ordered and spectrally-selective LC cells which each subtract or remove an orthogonal component of the visible spectrum. Examples of different configurations of subtractive or stacked color LCDs can be found in U.S. Pat. No. 5,032,007 to Silverstein et. al., U.S. Pat. No. 4,917,465 to Conner et. al., and U.S. Pat. No. 4,416,514 to Plummer. While successful as a full-color LCD light valve for projection displays in which the light rays passing through the stack of subtractive cells are collimated or at least telecentric, the subtractive or stacked LCD arrangement is not desirable for use with a backlit, direct-view LCD due to viewing-angle problems arising from the parallax produced by the relatively thick stack of spectrally-selective cells. For these reasons, spatial-additive color synthesis and the planar mosaic of color selection filters are preferred approaches to fullcolor direct-view color LCDs. Examples of mosaic color filters are shown in U.S. Reissue No. 33,882 to Morozumi, U.S. Pat. No. 4,987,043 to Roosen et al. and U.S. Pat. No. 5,066,512 to Goldowsky et al.
Conventional processing or creation of the patterned mosaic of color selection filters within the LC cell is costly, inefficient and severely limited by material compatibilities with the LC fluid. These filters are placed within the LC cell, which typically has a cell gap width on the order of 3 to 7 microns, in order to reduce viewing parallax in displays with small pixel dimensions. Placing the color selection filters outside of the LC cell would require that the filters be displaced from the pixel-forming apertures within the LC cell a minimum distance equal to the thickness of the LC cell glass, which is typically on the order of approximately 1100 microns. This would result in very significant viewing parallax between a pixel aperture and the associated color selection filter, such that at off-axis viewing angles light rays from an addressed pixel could easily go through the incorrect color selection filter (e.g., light rays from an addressed RED pixel aperture actually going through a GREEN color selection filter).
As such, there exists a need for improved color filter processing and placement; allowing easier processing, the use of more efficient filter materials, and increased color image quality over a larger viewing angle range. If an optical means could be developed to control or constrain the angles at which light propagated through the layers of a direct-view LCD until the final optical interface where the light rays may be expanded to provide a wide viewing angle (thereby effectively decoupling the LCD from the viewing orientation), then absorptive color selection filters could be placed outside the LC cell or highly-efficient, interference-type color selection filters could be employed. On either case, this would enable the color filters to be located on a different optical layer than the LC cell, processed using a wider range of more efficient color filter materials and processing stages, and should result in improved manufacturing yields, reduced production costs, and significantly improved LCD color performance and luminous efficiency.
Fiber-optic faceplates (FOFPs) have been used for contrast enhancement on special-purpose Cathode Ray Tube (CRT) displays, as light-collection elements on the front surface of reflective monochromatic LCDs to enhance the reflected luminance of the display, as light channeling elements for coupling patterned color phosphor mosaics to their respective pixel apertures in rear-illuminated color LCDs, and as image relay elements for coupling the output of image generation devices to photo-recording surfaces for hard-copy applications. Several patents relate to FOFPs. These include U.S. Pat. No. 4,344,668 to Gunther et al.; U.S. Pat. No. 4,349,817 to Hoffman et al.; U.S. Pat. No. 4,558,255 to Genovese et al.; U.S. Pat. No. 4,752,806 to Haas et. al.; U.S. Pat. No. 4,799,050 to Prince et al.; U.S. Pat. Nos. 5,035,490 and 5,181,130, both to Hubby, Jr; U.S. Pat. No. 5,050,965 to Conner et al.; U.S. Pat. No. 5,053,765 to Sonehara et al.; U.S. Pat. No. 5,113,285 to Franklin et al.; and U.S. Pat. No. 5,131,065 to Briggs et al.
Haas et. al. uses a FOFP to channel light emerging from an LC layer to a lens array and then to a photoreceptor. Genovese et. al. use a FOFP to channel light emitted by a vacuum fluorescent device to expose a photosensitive member for a printing device. These applications do not relate to direct-view display devices.
Briggs et. al. use a front FOFP to channel light emerging from an emissive phosphor layer to a viewer in order to create a high luminance and high contrast thin-film electro-luminescent display. Prince et. al. employ a FOFP as a light channeling element for coupling the emissions of a patterned color phosphor mosaic excited by an ultra-violet source to their respective pixel apertures in a rear-illuminated color LCD. These patents relate to the channeling of phosphor emissions in direct-view display devices and are not directly concerned with the improvement of off-axis viewing.
Hubby, Gunther et. al., and Hoffman et. al. all relate to reflective LCD devices that use a FOFP to collect incident light from a wider acceptance angle for the purposes of enhancing the reflected luminance and contrast of the display. This approach does not address the generation of color in an LCD and, in fact, is not applicable to a color LCD because there is not sufficient reflected luminance in such a LCD device to enable color separation and filtering and still provide enough output luminance for comfortable viewing. Moreover, this approach is not concerned with enhancing off-axis viewing performance.
Conner et. al. relates to a super-twisted nematic (STN) LCD that requires a collimated light source and uses sequentially-stacked subtractive color LC cells. The primary approach is intended for projection display applications. When applied to the direct-view situation, the display output requires decollimation or diffusion. This results in degraded image contrast and color desaturation under ambient illumination. This approach does not directly address high-performance, direct-view, transmissive TN color LCDs.
None of these references appreciate the problems overcome by the present invention.
U.S. Pat. No. 5,442,467, filed on Mar. 21, 1994 (issued on Aug. 15, 1995) by Silverstein et al., the subject matter of which is incorporated herein by reference, discloses a direct-view rear-illuminated LCD device, comprising: a backlight source; a rear diffuser layer; a rear polarizer; a LC cell including a rear glass layer with addressing elements and indium tin oxide (ITO) transparent pixel electrodes, a LC layer having a top and bottom surface, and a front FOFP as a front containing element of the LC cell and being located directly in contact with the top surface of the liquid crystal layer; a mosaic array of color absorption filters either deposited on the front face of the FOFP or located on a separate but adjacent substrate; and a front polarizer or analyzer. The front FOFP provides for a relatively narrow light acceptance solid angle (.theta..sub.Max IN) at a rear face adjacent the LC layer and a relatively wide light exit or output solid angle (.theta..sub.Max OUT) at a front face opposite the rear face. In addition, as described below, the FOFP provides azimuthal averaging of off-axis light, the implications of which will become apparent in subsequent paragraphs.
In a second embodiment of U.S. Pat. No. 5,442,467 the front polarizer or analyzer is located within the LC cell adjacent to the rear or input face of the front FOFP. This configuration provides for analysis of the polarization state of light exiting the LC cell prior to input to the front FOFP and is designed to eliminate the impact of any significant depolarization resulting from reflections within the FOFP fibers and thereby degrading display contrast. In this case, the front polarizer or analyzer may be a thin polarization coating or a thin film composed of aligned organic dye molecules that are deposited or bonded directly on the rear or input face of the front FOFP.
Third and fourth embodiments further add a rear FOFP, located between the diffuser and the LC cell, to the configurations of the first and second embodiments. The rear FOFP is opposite of the front FOFP and includes an input face, facing and adjacent to the diffuser, that provides a high .theta..sub.Max IN resulting in a relatively wide light input acceptance angle and an output face opposite the input face providing a low .theta..sub.Max OUT and resulting in a relatively narrow light exit or output angle. The principal objective of the rear FOFP is to provide increased collection of light from the rear illumination source, thereby providing an improvement in the luminous efficiency of the LCD.
Fifth and sixth embodiments further add a mosaic array of spectrally-selective color interference filters or holographic filters, located between the rear FOFP and the rear polarizer, to the configurations of the third and fourth embodiments. The principal objective of the mosaic array of color interference or holographic filters is to provide a narrow spectral bandpass matched to the primary red, green, and blue spectral emission peaks of the rear illumination source. These filters are spatially registered with the red, green, and blue elements of the pixel array and transmit narrow-band light to the appropriate pixel. Illumination outside of the spectral band of each filter is reflected back through the rear FOFP to the diffuser, which then reflects the light back to the filter array via the rear FOFP. Thus, the light is effectively "recycled" until it passes through a filter with the appropriate spectral bandpass. Since spectral interference and holographic filters are angle sensitive, the rear FOFP restricts the angle of incidence from the rear illumination source and diffuser. This additional array of color selection filters minimizes absorption losses in the primary color selection filter array at the front of the display device by restricting the spectral bandpass of light propagating through the LCD optical layers and color absorption filters of the primary color selection filter array, thereby providing an improvement in both the luminous efficiency and color performance of the direct-view color LCD.
U.S. Pat. No. 5,442,467 solves the LCD viewing angle problem by utilizing the front FOFP as a front cover plate and containing element of a LC cell, in direct contact with the LC fluid material or optionally an integral thin-film polarizer, eliminating a front glass substrate. This FOFP relays the polarized light rays emerging from the plane of the optically active LC material forward to another image plane at the exit apertures of the FOFP fibers. This effectively decouples the LC layer and other LCD optical layers behind the front FOFP from the viewing orientation of the display observer, in that the observer views the light rays emerging from the image plane relayed by the FOFP. If the rays propagating through the LC layer are only accepted by the FOFP through a narrow cone of angles (i.e., a low .theta..sub.Max IN), then the observer will only see the optical effects of the LC layer and other LCD optical elements as they would appear through a narrow viewing cone around the normal to the LCD regardless of viewing orientation relative to the coupled FOFP. If the light rays are made to diverge at the output from the FOFP or coupled additional layers of approximately index matched materials (i.e., a relatively high .theta..sub.Max OUT), then a relatively wide range of satisfactory viewing angles can be maintained for the transmissive direct-view display. The image formed by light rays propagating in a narrow cone of angles around the normal or perpendicular to the exit plane of the LC layer can then be viewed from any reasonable angle. In addition, the azimuthal averaging properties of the FOFP result in symmetrical viewing cones, effectively averaging out the typical LCD anisotropy. Since the image is relayed directly from the output of the LC layer by the FOFP, this configuration has the added benefit that absorptive color selection filters may be located at the output of the FOFP rather than in the LC cell itself. This may be accomplished by either direct deposition on the output surface of the FOFP or by placement of the filters on a substrate adjacent to the FOFP output surface. This simplifies filter processing and cell construction and enables greater latitude in the color filter materials which can be used as well as their spectral-selection performance.
The front and rear FOFPs comprise an array of individual optical fibers which are fused together with an interstitial cladding material and then cut and polished to a desired thickness to form a plate. The creation of FOFPs with varying optical characteristics is well known in the art. The optical fibers are designed to transmit through total internal reflection light incident at controlled input or acceptance angles while rejecting or absorbing light incident at larger angles. Light entering the fibers of the rear FOFP is collected over a wide acceptance angle .theta..sub.Max IN by use of a high numerical aperture (NA) FOFP and/or coupling to a boundary of low refractive index (e.g., air) and light exiting the optical fibers of the front FOFP is made to diverge or exit over a relatively wide angle .theta..sub.Max OUT also by use of a high NA and/or the ultimate coupling to a low refractive index boundary. FOFPs with low NAs and/or coupling to relatively high refractive index materials (e.g., plastic, polyimide, or optical glass) restrict the light output exit angle .theta..sub.Max OUT of the rear FOFP and the light input acceptance angle .theta..sub.Max IN of the front FOFP, respectively.
For purposes of the present invention, it should be understood that the term fiber-optic faceplate or FOFP is interpreted in its broadest sense as any material which embodies the essential optical properties of a FOFP. Thus, the functioning of the present invention is not dependent upon the use of a fused plate of optical fibers but rather on any material layer, including a fused plate of optical fibers, which is capable of total internal reflection, controllable NA at input and output surfaces, rotational azimuthal averaging and translation of the object plane from the back surface of the layer to the front surface of the layer. It should be apparent to those skilled in the art that these essential optical properties could be imparted to a range of materials, thus producing FOFP optical equivalents. These could include micro-machined or preformed glass or plastic substrates with a plurality of optical features, a variety of polymer networks containing a duality of materials with differing refractive indices or birefringence produced by physical alignment or stress, or any other approach able to result in a substrate containing a plurality of cylindrical features whose boundaries are defined by a discontinuity of refractive indices.
The combination of low and high .theta..sub.Max IN and .theta..sub.Max OUT at the appropriate interfaces along with the azimuthal averaging property as described below creates remarkable property results. An observer can view the display at a relatively large range of viewing angles with only minimal variation in LCD image contrast and chromaticity as a function of viewing angle, unlike the inhomogeneities and anisotropies observed with a typical direct-view transmissive color LCD. Further, light from a rear illumination source is allowed to enter the rear FOFP at a relatively wide acceptance angle that is channelled down to a relatively narrow exit angle as it reaches the output face of the rear faceplate and travels through the display optics. Once past the output face of the rear FOFP, the light is in a relatively narrow beam as it travels through the optics. Then, when it reaches the output face of the front FOFP the beam is again expanded to a relatively wide cone or solid angle, providing a wide viewing angle. Thus, the use of the rear FOFP achieves an increase in the amount of light collected from the source and transmitted through the LCD optics, thereby providing some improvement in the luminous efficiency of the display over the single front FOFP configuration of the invention.
The important features controlling .theta..sub.Max IN and .theta..sub.Max OUT are the NA of the FOFP and the refractive index of optical materials or layers at the boundary with the FOFP. The NA is a value which expresses the light gathering power of an optical fiber in much the same manner as the f/# number of a lens system. The basic relationships between NA, .theta..sub.Max, and the refractive index (N) of boundary materials or layers are described in the following equations that are well known in the art: ##EQU1## where: NA=numerical aperture of FOFP
.theta..sub.max =FOFP maximum solid angle of acceptance or exit PA1 N.sub.o =refractive index of surrounding material or boundary PA1 N.sub.fib =refractive index of optical fiber PA1 N.sub.clad =refractive index of fiber cladding PA1 .theta..sub.inc =angle of incidence PA1 N.sub.1 =refractive index of first optical media PA1 N.sub.2 =refractive index of second optical media PA1 PD=pupil diameter PA1 V.sub.d =viewing distance PA1 N.sub.FOFP =refractive index of FOFP PA1 t=distance from entrance plane of FOFP to object plane. PA1 Where: PA1 d.sub.a =outer diameter of annulus projected on the surface plane PA1 .theta..sub.max =half-angle of maximum acceptance cone for FOFP entrance surface PA1 t=distance from entrance plane of FOFP to the surface plane ##EQU4## Where: w.sub.a =width of annulus projected on the surface plane PA1 .theta.=angle from normal to the FOFP PA1 t=distance from entrance plane of FOFP to the surface plane PA1 N.sub.FOFP =refractive index of FOFP PA1 PD=pupil diameter PA1 V.sub.d =viewing distance
It is also necessary to calculate the angle of refraction for light rays that exit the FOFP, propagate through several optical layers, and finally exit the LCD at the final optical interface with air. For these rays, the angle of refraction can be calculated for each optical boundary and a final estimate obtained for the angular distribution of light at the exit of the LCD. The following equation enables the calculation of the angle of refraction at the boundary between two optical media having indices of refraction N.sub.1 and N.sub.2, where N.sub.1 is the refractive index of the first media and N.sub.2 is the refractive index of the second media: ##EQU2## where: .theta..sub.ref =angle of refraction
Thus, it can be seen that the numerical aperture of a FOFP is a function of the refractive indices of the optical fibers (N.sub.fib) and cladding (N.sub.clad), while the light acceptance solid angle (.theta..sub.Max IN) and the light exit or output solid angle (.theta..sub.Max OUT) of a FOFP are also a function of the refractive indices (N.sub.o) of the material(s) at the respective boundaries of the FOFP. For the present invention, preferred values for .theta..sub.Max to provide a low or narrow angular distribution of light are .theta..sub.Max .ltoreq.30.degree. and preferred values for .theta..sub.Max to provide a high or wide angular distribution of light are .theta..sub.Max .gtoreq.50.degree..
These relations are illustrated in FIG. 1 for a typical optical fiber 10. Light enters the optical fiber 10 within the cone 12 defined by .theta..sub.max and is totally internally reflected to propagate down the length of the fiber 10 essentially without loss. If the relative index of the material surrounding the fiber 10 at the entrance and exit surfaces (N.sub.o) is the same, then the light will exit the fiber 10 at the same angle .theta. at which it entered. Light which enters the fiber 10 outside of the cone 12 defined by .theta..sub.max is not fully guided through the length of the fiber 10 and "leaks" out of the fiber 10 into the adjacent cladding material 14.
The light rays, which are either unguided or partially guided, may pass through the cladding material 14 and enter other fibers in a fiber-optic bundle or fused faceplate but typically leak out of these fibers as well and continues to traverse the bundle or faceplate. FIGS. 2a and 2b show the effects of varying the numerical aperture of a fiber 10. FIG. 2a shows a fiber 10 having a small numerical aperture and thus a smaller light acceptance cone 12a. FIG. 2b shows a fiber 10 having a large numerical aperture and thus a larger light acceptance cone 12b. Thus, the higher the numerical aperture of the fiber 10, the larger .theta..sub.max at the entrance and exit.
In general, light which enters the optical fiber 10 is rotated about the central axis of the fiber as it propagates along the length of the fiber. Thus, light which enters at a given angle .theta. from the normal to the fiber input surface exits the fiber at the same exit angle .theta., but at a rotated azimuthal position .phi.. This rotation is dependent on the number of reflections within the fiber 10 and also by the internal surfaces of the fibers. Skew rays typically undergo more rotation than meridional rays. For the application of FOFPs to LCDs, most of the illumination entering the fiber will be skew rays.
As explained above, in fused fiber optic bundles and faceplates, both guided and unguided rays undergo azimuthal rotation due to the curved fiber surfaces. As shown in FIG. 3, the consequence of this rotation is that the optical fiber 10 averages about the azimuthal position .phi. all of the incoming light 11 entering at a given declination angle .theta. such that the output consists of a hollow cone 16 with a solid angle of 2.theta.. Since the light emerging as a hollow cone 16 consists of an average about the azimuthal position .phi., the transmitted light intensity is equal at all azimuthal angles .phi.. it is this property of azimuthal averaging that enables FOFPs to produce symmetrical viewing characteristics over wide angles when coupled to a LCD with inherent anisotropies in luminance and contrast.
An important consideration in interpreting the effects of any light stimulus is the effective light acceptance cone of the eye and of instruments designed to measure the effective light stimulus for vision such as photometers and spectro-radiometers. The acceptance cone of the eye is quite small. That is, the solid angle .theta. through which light can enter the eye is narrow. In other words, the eye has a small numerical aperture. FIG. 4 illustrates the small light acceptance cone of the eye 20 and the parameters that determine this angle such as the diameter of the eye's entrance pupil and the viewing distance. The acceptance cone may be calculated as the arctan (pupil diameter/viewing distance). The pupil distance can generally be referred to as the distance between the pupil (aperture stop) 22 and the retinal image plane 24. The viewing distance is the distance between the pupil 22 and a surface plane 18. For a nominal 3 mm pupil diameter and a 508 mm viewing distance, the acceptance cone is approximately 0.34 degrees. Similar geometric considerations apply to photo-optic measurement instrumentation. Thus, for any given point of visual fixation on a surface plane 18 (e.g., a display or object), the eye 20 accepts only a small portion of the angular distribution of light emitted or reflected from that surface plane 18.
As a result of the azimuthal averaging properties of FOFPs, spatial averaging of information from the surface plane 18 also occurs to produce low-pass spatial filtering of information. Assuming the refractive indices of the FOFP and the first optical layer of the LCD (e.g., polarizer) are closely matched, the degree of such low-pass spatial filtering is a function of the viewing angle, the distance from the entrance of the FOFP to the surface plane, the light acceptance cone of the eye, and the refractive indices of the FOFP and the viewing medium (i.e., air). FIG. 5 depicts the geometrical factors associated with the spatial averaging arising from the coupling of a FOFP 24 to a LCD 32. For on-axis viewing from the eye 20, the information from the LCD 32 is averaged within the projected area defined by the acceptance cone of the eye 20, the distance from the LCD 32 to the entrance plane of the FOFP 24, and the ratio of the refractive indices of the viewing medium (N.sub.m =1.0 for viewing in air) and the FOFP 24. Cone 27 shows the cone of spatial averaging for on-axis viewing angle from eye 20. The following equation describes the region of spatial averaging for on-axis viewing: ##EQU3## Where: d=diameter of projected area on surface plane
For the geometry shown in FIG. 5 with t=200 microns, a pupil diameter of 3 mm, a viewing distance of 508 mm, and a FOFP refractive index of N=1.5, the spatially-averaged region is equal to 0.79 microns. This degree of low-pass filtering will not be perceptible, and thus not provide any useful attenuation of high-spatial frequency noise produced by the LCD pixel geometry. However, the low-pass filtering caused by on-axis spatial averaging within the FOFP will not produce visible image degradation.
The maximum spatial averaging will occur with a viewing angle equal to .theta..sub.max of the FOFP 24. This situation is also depicted in FIG. 5 from eye 21. For the case of spatial averaging for off-axis viewing from eye 21, the LCD information will be averaged within a circular annular region whose outer diameter is that of the hollow cone corresponding to the angle .theta..sub.max on the inner or entrance surface of the FOFP 24 and whose width is determined by the light acceptance cone of the eye 21, the angle of view relative to the normal to the FOFP surface (.theta.), and the ratio of the refractive indices of the viewing medium (N.sub.air =1.0) and the FOFP. Cone 28 shows the cone of spatial averaging for off-axis viewing angle from eye 21. The following relations describe spatial averaging for the off-axis viewing situation: EQU d.sub.a =2 tan .theta..sub.max t
As an example of the off-axis spatial averaging effect, consider again the geometry shown in FIG. 5 with t=200 microns, PD=3 mm, V.sub.d =508 mm, a FOFP refractive index of approximately N=1.5 with a NA=0.66, and a polarizer 30 with a refractive index of 1.5 bounding the entrance surface of the FOFP 24. For this situation, .theta..sub.max at the FOFP entrance surface will be 26.1.degree. and the outer diameter of the annular spatially-averaged region is equal to approximately 196 microns. The angle .theta..sub.max at the FOFP exit surface is about 41.3.degree. which corresponds with the viewing angle from the normal to the FOFP (.theta.). The resulting width of the annular spatially-averaged region is about 0.59 microns.
The spatial averaging of pixel information within an annular region of the surface plane is not a desirable characteristic of fiber optics. However, given the minimal distances between the surface plane and the entrance plane of the FOFP when coupled to an LCD 26, the effects of annular spatial averaging in off-axis viewing should provide only minimal degradation of the display image.